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131 lines
3.5 KiB
Go
131 lines
3.5 KiB
Go
// Copyright ©2016 The gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package native
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import (
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/lapack"
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)
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// Dorgql generates the m×n matrix Q with orthonormal columns defined as the
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// last n columns of a product of k elementary reflectors of order m
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// Q = H_{k-1} * ... * H_1 * H_0.
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//
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// It must hold that
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// 0 <= k <= n <= m,
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// and Dorgql will panic otherwise.
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//
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// On entry, the (n-k+i)-th column of A must contain the vector which defines
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// the elementary reflector H_i, for i=0,...,k-1, and tau[i] must contain its
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// scalar factor. On return, a contains the m×n matrix Q.
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//
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// tau must have length at least k, and Dorgql will panic otherwise.
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//
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// work must have length at least max(1,lwork), and lwork must be at least
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// max(1,n), otherwise Dorgql will panic. For optimum performance lwork must
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// be a sufficiently large multiple of n.
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//
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// If lwork == -1, instead of computing Dorgql the optimal work length is stored
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// into work[0].
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//
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// Dorgql is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dorgql(m, n, k int, a []float64, lda int, tau, work []float64, lwork int) {
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switch {
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case n < 0:
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panic(nLT0)
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case m < n:
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panic(mLTN)
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case k < 0:
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panic(kLT0)
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case k > n:
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panic(kGTN)
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case lwork < max(1, n) && lwork != -1:
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panic(badWork)
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case len(work) < lwork:
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panic(shortWork)
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}
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if lwork != -1 {
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checkMatrix(m, n, a, lda)
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if len(tau) < k {
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panic(badTau)
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}
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}
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if n == 0 {
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work[0] = 1
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return
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}
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nb := impl.Ilaenv(1, "DORGQL", " ", m, n, k, -1)
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if lwork == -1 {
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work[0] = float64(n * nb)
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return
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}
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nbmin := 2
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var nx, ldwork int
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iws := n
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if nb > 1 && nb < k {
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// Determine when to cross over from blocked to unblocked code.
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nx = max(0, impl.Ilaenv(3, "DORGQL", " ", m, n, k, -1))
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if nx < k {
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// Determine if workspace is large enough for blocked code.
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iws = n * nb
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if lwork < iws {
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// Not enough workspace to use optimal nb: reduce nb and determine
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// the minimum value of nb.
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nb = lwork / n
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nbmin = max(2, impl.Ilaenv(2, "DORGQL", " ", m, n, k, -1))
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}
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ldwork = nb
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}
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}
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var kk int
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if nb >= nbmin && nb < k && nx < k {
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// Use blocked code after the first block. The last kk columns are handled
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// by the block method.
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kk = min(k, ((k-nx+nb-1)/nb)*nb)
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// Set A(m-kk:m, 0:n-kk) to zero.
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for i := m - kk; i < m; i++ {
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for j := 0; j < n-kk; j++ {
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a[i*lda+j] = 0
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}
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}
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}
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// Use unblocked code for the first or only block.
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impl.Dorg2l(m-kk, n-kk, k-kk, a, lda, tau, work)
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if kk > 0 {
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// Use blocked code.
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for i := k - kk; i < k; i += nb {
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ib := min(nb, k-i)
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if n-k+i > 0 {
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// Form the triangular factor of the block reflector
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// H = H_{i+ib-1} * ... * H_{i+1} * H_i.
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impl.Dlarft(lapack.Backward, lapack.ColumnWise, m-k+i+ib, ib,
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a[n-k+i:], lda, tau[i:], work, ldwork)
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// Apply H to A[0:m-k+i+ib, 0:n-k+i] from the left.
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impl.Dlarfb(blas.Left, blas.NoTrans, lapack.Backward, lapack.ColumnWise,
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m-k+i+ib, n-k+i, ib, a[n-k+i:], lda, work, ldwork,
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a, lda, work[ib*ldwork:], ldwork)
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}
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// Apply H to rows 0:m-k+i+ib of current block.
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impl.Dorg2l(m-k+i+ib, ib, ib, a[n-k+i:], lda, tau[i:], work)
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// Set rows m-k+i+ib:m of current block to zero.
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for j := n - k + i; j < n-k+i+ib; j++ {
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for l := m - k + i + ib; l < m; l++ {
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a[l*lda+j] = 0
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}
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}
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}
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}
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work[0] = float64(iws)
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}
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